Example

Based on the previous example, can you guess the graph of $y=x^2-1$.

Solution

In the last example, we looked at the equation $y=x^2$ and its graph. In this example, each corresponding $y$-coordinate is one less than in the last example. Imagine keeping each $x$-coordinate fixed and decreasing each $y$-coordinate by $1$. The affect will be to shift the entire graph down one $1$ unit. The graph will have the same shape---it will simply be translated down one unit.